Carnap's syntactic frameworks, as purely formal rule-governed calculi, cannot themselves specify which physical domain a given mathematical structure maps onto, leaving the correspondence relation unexplained.

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Carnap: Rudolf Carnap (1891-1970) was a highly influential German-American philosopher who believed that many traditional philosophical problems could be solved by carefully analyzing the language we use to talk about them. He pioneered the idea that philosophy should work closely with science and mathematics, using precise logical methods to clarify confused thinking. His work fundamentally changed how philosophers approach their discipline, making language analysis and logical rigor central to philosophical practice.
Formal rule-governed calculi(how syntactic frameworks operate): A purely abstract system with strict, precisely-defined rules (like the rules of math) that tells you how to manipulate symbols, without any connection to the real world yet.
Maps onto(logic and mathematics in philosophy): Corresponds to or matches up with; when one thing 'maps onto' another, there's a systematic relationship between them.
Mathematical structure(what structural realists claim is what we actually know about reality)

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